论文标题
双线性strichartz的kdv方程式估计
Bilinear Strichartz estimates for the KdV equation on the torus
论文作者
论文摘要
在本文中，我们考虑了周期性KDV方程的双线性strichartz估计值。我们对$ p = 8 $的false $ l^p $ strichartz估计的具体反例，至少对于lebesgue指数$ p $ $ p $。此外，我们证明了biinear strichartz在不同频率区域中的估计，这代表了一种平滑的效果。当该周期趋于无穷大时，圆环上的strichartz估算的频率本地化版本匹配了真实的线设置中的频率。另外，四分之一的广义KDV方程被视为应用程序。
In this paper, we consider the bilinear Strichartz estimates for the periodic KdV equation. We give a concrete counterexample to the false $L^p$ Strichartz estimates for $p=8$, at least for a subset of the range of Lebesgue exponents $p$.Moreover, we prove the bilinear Strichartz estimate in different frequency regions, which represents a kind of a smoothing effects. When the period tends to infinity, the frequency localized version of Strichartz estimate on the torus matches to the one in the real line setting. In addition, the quartic generalized KdV equation is considered as an application.
